Question

The model represents the factorization of 2x2 + 5x + 3. What is the missing term in the factorization of 2x2 + 5x + 3? (2x + 3)(x + )

Answer 1

Answer: The missing term in the factorization will be (x+1).

Explanation:

Since we have given that

$2x^2+5x+3$

We'll use splitting the middle term in which we have given the quadratic equation as

$ax^2+bx+c=0$

Now, we have to find the two integers whose product will be 'ac' and whose sum will be 'b'.

By splitting the middle term , we get,

$2x^2+3x+2x+3\\\\=x(2x+3)+1(2x+3)\\\\=(x+1)(2x+3)$

Hence, the missing term in the factorization will be (x+1).

Answer 2

we have

$2x^{2} + 5x + 3$

equate the expression to zero

$2x^{2} + 5x + 3 =0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$2x^{2} + 5x =-3$

Factor the leading coefficient

$2(x^{2} + 2.5x) =-3$

Complete the square. Remember to balance the equation by adding the same constants to each side

$2(x^{2} + 2.5x+1.5625) =-3+3.125$

$2(x^{2} + 2.5x+1.5625) =0.125$

Rewrite as perfect squares

$2(x+1.25)^{2} =0.125$

$(x+1.25)^{2} =0.0625$

$(x+1.25) =(+/-)\sqrt{0.0625} \\ x1=-1.25+\sqrt{0.0625}\\ x2=-1.25-\sqrt{0.0625}$

Simplify

$x1=-1.25+\sqrt{0.0625}\\ x1=-1.25+0.25\\ x1=-1$

$x2=-1.25-\sqrt{0.0625}\\ x2=-1.25-0.25\\ x2=-1.50$

$2x^{2} + 5x + 3=2(x+1.5)(x+1)\\ =(2x+3)(x+1)$

therefore

the answer is

the missing term in the factorization is $1$